• To explain how ocean surface currents affect the path of
floating objects.

• To describe how early mariners navigated the ocean based on
speed and direction.

• To track Columbus’s first voyage to America, and Bligh’s mutiny
survival.

• To describe the role of ocean explorers in gathering
scientific information.

Introduction: How Did They
Do That?

“Historians believe that Pacific Islanders explored the entire South Pacific well before the era of recorded history.
Historians speculate around 2500 B.C., Southeast Asians began to migrate
throughout the Pacific.1” Their 30.5 meter long canoes, shown
on the left, were navigated by men who were taught from childhood to decipher
nautical information including star positions, ocean currents, wave echoes,
prevailing winds, and the habits of migratory birds. “More than 1,300 years
ago, Polynesian explorers set out from Havai’i (now Raiatea, in the Society islands) in great
double-hulled canoes to cross the vast unknown expanse of the North Pacific
Ocean. By chance, they discovered and subsequently colonized, the Hawaiian
Islands. A long canoe voyage across the uncharted ocean must have required an
exceptional degree of navigational skill. By observing the stars, winds and currents,
ancient navigators could approximate their geographic position.2”

Ocean surface currents have played
an important role in navigation from ancient times, through the exploration of
the world by sail to present day shipping. Today, most ships are propeller-driven
and less dependent on the winds, but all ships benefit significantly when
carried by ocean surface currents.

In
Lesson 1, you will experiment with the effects of ocean surface currents on drifting
objects.You will use a simple
computer model to investigate the movements of objects drifting on the ocean
surface. You will also learn how Columbus sailed to the new world using tools such as a compass, an astrolabe, an hourglass, maps, and charts, dead
reckoning, winds and currents. You will read Captain William Bligh’s journal
and find out how he survived after the mutiny on his ship the Bounty, when he
was set to sea, in a small boat, near Tahiti without any instruments.

Before beginning this lesson is
it helpful to learn how much information you already know about Navigation. A
simple preconceptions survey has been created for you to assess your prior
knowledge.

1. Click on the blue Quiz button below.

2. Take the quiz

3. Submit your responses online
and they will be automatically scored.

4. Return to this guide and
begin your exploration of the Coriolis Force.

A Drifter Model

How do ocean surface currents
affect the motion of floating objects?

Propelled by winds, and steered
by Earth’s rotation and gravity, the waters in the world’s ocean are constantly
in motion. Water moves horizontally (east, west, north and south) and
vertically (sinking and rising). The following investigation focuses on the
horizontal circulation of water at the ocean surface. The waters of the ocean
are stratified by gravity so that water found at greater depths is typically
denser (colder, saltier) than surface waters. This stratification inhibits
mixing of the layers and decouples surface motion from the deeper waters. A
simplistic model for surface currents would imagine them as a thin layer of
circulating ocean water above more static, deeper layers.

What is a Drifter Model?

In order to experiment with
drifting objects carried by ocean surface currents, you will use a computer
model. The model uses historical monthly, ship drift
data, which was gathered about ocean surface current circulation and simple
physics equations of motion to predict drifter motion. The OSCAR visualizer, located in this site, contains more recent and accurate sources of
ocean surface current data. OSCAR data will be used in lessons 5 & 6.

The drifter database consists of
the following values for locations on the ocean surface:

• East-west (zonal) mean
velocity component, u, and an
estimate of its variability.

• North-south (meridional) mean
velocity component, v, and an
estimate of its variability.

For example, a value for u in a specific month and location
might be 0.3 meters/second with a variability of 0.1 meters/second. In simple
terms, the mean or average zonal current moved eastward at 0.3 meters (about 1
foot) in one second, on any given day. The actual current might vary by 0.1
meter per second above and below this value. Commonly observed zonal currents
might fall in the range 0.2 to 0.4 meters/second.

Click Ship Drift Modelto link to the model on your computer. This model accounts for the
circulation of currents and does not include effects of wind/waves or the
dynamics of the floating object. The drifter is imagined as a small object
floating at the surface, with a density near that of seawater. The model does
not apply to sailing or motorized ships.

The Ship Drift Model page, shown below, displays a map of the world
with arrows depicting the mean or average direction of currents at the ocean
surface. The current patterns are fairly complex and show the effects of
continental landmasses. The arrows indicate the direction of the current and
the arrow colors indicate the speed of the current. Below the map, there is a
color scale that provides the key for converting each yellow, green, red, or
blue arrow to a speed in meters per second.

1. Look carefully at the world map below (or on your computer
screen), to find the speeds corresponding to colored arrows. Fill in the empty
boxes with current speeds.

Arrow

Color

Dark

Blue

Light

Blue

Green

Yellow

Orange

Red

Dark Red

Current

Speed

(m/s)

Using the Ship Drift Model on your computer

Look at the bottom of the data
visualizer. There are three options, 1. Latitude/longitude,

2. The month selection and 3.
The Pop-up Map.

• To find the latitude and
longitude of a point on the map, roll the mouse over the map. The latitude and
longitude for that point will appear in the box at the bottom of the currents
map.

• To view currents in greater
detail, choose a month from the drop-down menu on the left, and then click the
Pop-up Map button on the right and a large, zoomable map will pop up in a
separate window. The Pop-up map will be helpful in tracing surface current
circulation.

• To start your drifters voyage,
move the computer mouse cursor over the ocean and click on the map. A second
window with a map showing the tracks of five drifters will pop up.

In the example shown below, the
start click was made near the southeast coast of the United States. A square,
black, outline box marks the beginning of the drifter’s voyage (labeled in the
image with the word “Start”). The colored tracks (purple, blue, red, orange,
blue) follow five drifters under the influence of variable currents through
five years. A color-coded, diamond-shaped, outline box marks the end of each
track. The five different tracks show the approximate effects of the ocean
surface current variability.

Coordinates on the map below use
degrees of longitude (horizontal scale) and degrees of latitude (vertical
scale). The starting point has a longitude near -80o and latitude
near 31o.

2. Estimate the end locations for the five drifters and write the
number in the table below.

Drifter color

Blue

Green

Orange

Red

Purple

End longitude

End latitude

Experiment With Your Own Drifter

Try creating your own voyager
drifter. Use the main map of the Ship Drift Model as well as

the higher resolution map to
select a starting site and make a prediction of where your drifters will
travel.

3. Starting Longitude _____________ Starting Latitude ______________

4. Sketch your prediction for the drifter’s track on the map on the
next page. In case of uncertainty, trace several possible routes.

5. Click your selected starting location on the map. Estimate the end locations of each of the
five drifters:

Drifter color

Blue

Green

Orange

Red

Purple

End longitude

End latitude

6. How well does your estimate of the drifter route agree with the
computer model? Where is there
agreement? Where do predictions disagree
the most?

Rubber Duckies
Venture Around The World

What do you know about the flow of currents around the
world?

Many tools are used to study the flow of the ocean. Curt Ebbesmeyer,
pictured on the left with tub toys, says
that when investigating the paths of ocean surface currents, he uses every tool
available. He studies satellite images and data from buoys.
He tosses objects into the water to see where they go.

In January 1992, his toolbox grew
even larger. A storm washed several containers from a ship bound from Hong Kong
to Tacoma, Washington. One container carried 29,000 bathtub toys. Ten months
later, plastic ducks, turtles, frogs, and beavers began washing up near Sitka,
Alaska. A new experiment had begun and Curt’s career as a pioneer in the study
of floating debris was in full swing.

Today, Curt presides over a
network of thousands of beachcombers. These volunteers and hobbyists walk the
beaches of the world, snatching up shoes, hockey equipment, surveyor stakes,
bowling balls, Lego’s, tobacco jars, utility poles, fishing gear, survival
suits (with and without body parts), and the occasional message in a bottle,
and report their findings to Curt. Curt studies the information, thinks about
what it all means, and compiles these stories into a newsletter, Beachcombers
Alert, which he mails to his subscribers four times a year. If a new cargo
spill occurs, Curt alerts his network about what to look for.

Read more about Curt by clicking on his name in the first
paragraph.

Dead Reckoning

How can one navigate—determine location—on
the open ocean?

When not
using the stars, Sun or moon to determine their location, sailors and explorers
navigated by deduced (or dead) reckoning. This was the method used by Columbus and most other sailors of his era. In dead reckoning, the navigator finds his
position by measuring the course and distance he has sailed from some known
point. Starting from a known point, the navigator measures out his course and
distance from that point on a chart, pricking the chart with a pin to mark the
new position. Each day's ending position would be the starting point for the
next day's course-and-distance measurement. For this method to work the navigator
needed a way to measure his course and to measure the distance sailed. Course
was measured by a magnetic compass, which had been known in Europe since at
least 1183. Distance was determined by a time and speed calculation: the
navigator multiplied the speed of the vessel by the time traveled to get the
distance.

7. To determine speed on old sailing boats, sailors often used a log line.
Describe how a log line was used and make a drawing of a log line on the back
of this sheet.

The fundamental flaw in using this log line method to determine distance is
that it does not account for the effects of surface currents. The log line
method measures the speed of the ship relative to the surface water. It
provides no means to estimate how fast the water itself flows. If a boat is
carried westward by a strong current, the log line method will not reveal the
existence of the current. If you travel steadily on a train along a straight
track, you will barely be aware that you are in motion relative to the tracks.
This fact is related to Newton’s First Law of Motion, which states that steady
motion in a straight line is “natural” and undetectable without reference to an
outside reference object.

8. How do you think a
speedometer on a car measures speed? Are there any circumstances that might
cause this measurement to be incorrect and not reveal the “true” speed of the
car?

To determine their direction of travel, sailors used the compass. The
compass is a magnet with ends labeled N and S. The N end points to the north
magnetic pole of the Earth. This pole is situated in northern Canada and does
not coincide with the north geographic pole (the “North Pole”). True north lies
along Earth’s axis of rotation and points in the direction of Polaris, the
North Star.

9. Click the link to “Magnetic
Declination” and write a definition of it. Include a drawing that shows the
difference between geographic north and magnetic north.

To plot their track on a map, sailors
observed the heading or direction their ship traveled. They then compared their
heading to the magnetic North direction revealed by a compass. Sailors were
aware that the magnetic declination did not represent true north, so to
compensate, they tried to map magnetic declinations around the globe. North as
measured by the compass typically is off by several degrees; this variation
depends on location and changes over decades.

Both the log line and the compass provided sailors with the means for
deduced reckoning (frequently abbreviated ded or dead reckoning) so they could
at least approximately reconstruct their travels. On the ocean, this task is crucial for
survival and success since there are few stable landmarks in a fluid
environment.

10. You may be accustomed to using deduced reckoning when you travel from one place
to another. For example, suppose you are in a car or train and judge that you are “30
minutes from downtown.” What simple assumptions does this make about your
travel? Write your answer in the space below.

Closed loop survey

To
practice and test your skills of measurement and deduced reckoning, try
conducting a closed loop survey activity. This
activity can be done on a small desktop, as well as outside. Making
measurements of your travels in a closed loop, where you end up at the point
where you started provides a simple check of navigation methods. If you come
back to the same point, your measurements should determine a path that draws a
closed loop.

Sailors
knew that surface currents affected the accuracy of their navigation
predictions. They called the difference between their deduced and
astronomically determined positions, ship drift.
Astronomical determination of positions on Earth using the Sun and the stars is
possible because the stars appear fixed and the Sun follows a cyclical,
predictable motion. The measured differences between positions determined by
dead reckoning and astronomical methods provided the earliest estimates of
ocean surface currents.

The Astronomical Fix

How
can you determine where you are located on planet Earth?

The
stars, moon, and Sun provide reference points necessary to determine one’s
position accurately. As Earth rotates, the astronomical objects follow a path
in the sky. The time they reach determined positions may be used to determine
your longitude and latitude.

Our Earth is a sphere, and angles are used to specify the location of sites
on the surface of the Earth. In the east-west direction, one measures longitude
with 0o set at Greenwich, England. Moving westward (towards
America), longitude angles are negative: between -180o and 0o.
Moving eastward (towards Europe, the Middle East and Russia), longitude angles
are positive: between 0o and +180o.

In the north-south direction, one measures latitude with 0o set
at the equator of Earth. Northward (towards the North Pole), positive
latitude angles are between 0o and 90o. Southward
(towards the South Pole), negative latitude angles are between -90o and 0o.

Over the course of 24 hours, Earth rotates through 360 degrees, and the
stars appear to rotate in the opposite direction. The positions of the stars,
moon and Sun in the sky at any specific time, depends on your location. By carefully
measuring both the positions of astronomical object positions and the times,
you can find your latitude and longitude. This is called an "astronomical
fix".

Find Your Place In The Sun by measuring your longitude and latitude.

The easiest times to determine one’s position are when the astronomical
bodies pass overhead or reach their highest elevation above the horizon. Solar
noon is when the Sun is highest in the sky. On a clear day, it is easy to
determine the time of solar noon. As an investigation, measurements
of the Sun around solar noon may be used to determine longitude and latitude.

The Columbus Voyages

How can we track a voyage of Columbus?

In celestial navigation, the navigator observes celestial
bodies (Sun, Moon and stars) to measure latitude. (In Columbus's day, it was
usually impossible to measure one’s longitude.) Even in ancient times, it was
fairly easy to find one’s latitude by looking at the Sun and stars, as long as
one wasn’t too concerned about accuracy. Each star has a celestial latitude or
declination. Knowing the declination of a star that is directly overhead
enables you to know your latitude on earth. Even if a star isn't directly
overhead, by measuring the angle between the star and the overhead point
(called the zenith), you can still determine your latitude — provided you
measure the star at the time of night when the star is highest in the sky.

Use Table 1 (below) to re-create
Columbus’s travels with the Voyager model. To
make the re-creation as accurate as possible, this model provides three tools:
ocean current data, a historical model of Earth’s magnetic field, and physics
kinematic equations to trace a ship’s movements. Because the ocean currents of
Columbus’s time are unknown, this model uses monthly surface current data based
on ship drift observations made mostly in the 20th century. Observed current fluctuations
(i.e., the “Variable Current” in the model) are simulated with random numbers.
This model does not simulate the effect of winds. Rather, it uses speeds
measured by Columbus and his crew. These log-line speeds reflect both the wind
conditions and the way the ship was being sailed.

To determine his direction (or
heading), Columbus relied on a compass, and his readings were not corrected for
the difference between magnetic north and the geographic north. The Voyager
model includes a magnetic model that predicts Earth’s magnetic field on Earth’s
surface between 5000 BC and 1950 AD.

Historical records provide
navigation details about the voyages of Columbus. Table 1 is based on
Columbus’s record of his first voyage to the Americas. Values have been
adapted, and simplified, with permission, from the website of Keith A.
Pickering

11. Begin a simulation of Columbus’s voyage by manipulating the Voyager model and
record the values for longitude and latitude for 34 days in 1492 in table 1. On
the left side of the model, you will input the following:

• Year: 1492

• Month: September

• Initial Longitude: -17.0

• Initial Latitude: -28.0

• Compass Heading

• Log Line Speed (meters/second) as
indicated in Table I for each of the days.

• After putting
in the data for the first day, click the Start button.

• For each
following day, enter the compass heading and logline speed from the table
and click continue.

The columns on the right side of
the model control panel show, current, longitude and latitude at the day’s end
and magnetic field information. The magnetic variation is labeled as the
“magnetic field declination”. Record the final longitude and latitude values in
Table 1.

Table 1 – Recreating Columbus’s
First Voyage to America

Starting Longitude and Latitude -17.0, 28.0

1st Column

Dates

Compass

Heading

Speed

(m/s)

Final

Longitude, Latitude

2nd Column

Dates Continued

Compass

Heading

Speed

(m/s)

Final

Longitude, Latitude

Sep 8

270

0.52

Sep 25

234.4

1.23

Sep 9

277.7

3.09

Sep 26

261.3

1.77

Sep 10

270

3.43

Sep 27

270

1.37

Sep 11

270

2.52

Sep 28

270

0.80

Sep 12

270

1.89

Sep 29

270

1.37

Sep 13

270

1.89

Sep 30

270

0.80

Sep 14

270

1.14

Oct 1

270

1.43

Sep 15

270

1.83

Oct 2

270

2.23

Sep 16

270

2.23

Oct 3

270

2.69

Sep 17

270

2.86

Oct 4

270

3.61

Sep 18

270

3.15

Oct 5

270

3.26

Sep 19

270

1.43

Oct 6

270

2.29

Sep 20

271

0.52

Oct 7

266

1.60

Sep 21

270

0.92

Oct 8

247.5

0.66

Sep 22

292.5

2.06

Oct 9

248.2

1.80

Sep 23

315

1.83

Oct 10

247.5

3.38

Sep 24

270

0.83

Oct 11

257.7

2.83

2.67 nautical mile = 1 league; 1 nmi = 1852 meters

Final Longitude and Latitude: -73.7, 22.2

12. When you have
completed recording all longitudes and latitudes, use these values and trace
the simulated voyage on the map below.

Note: If you repeat the voyage or have
several teams of students use the model; you will notice that the final
predicted location (longitude and latitude) of the ship on October 11 varies.
This variation is due to the measured uncertainty in the current data. The
model deliberately simulates current fluctuations unless you turn off this
feature by setting Variable Current to “No."

You may use the same model to simulate a
voyage that begins from a location anywhere else on the globe. With no
knowledge of the wind conditions at another site, you might set the “log line”
speed to Columbus’s mean speed.

Voyage Speeds

What can we learn from Columbus’s recorded speeds?

The mean speed of Columbus’s voyage was 1.91
m/s. This speed was measured with a log line device and does not include ocean
surface currents. Unlike today’s self-powered boats, which burn coal, gas or
oil, Columbus’s boats relied on wind power. Wind power has the disadvantage
that it is variable, but has the advantage that it is freely available. The
figure, on the right, shows a histogram of the voyage speeds: the horizontal
axis shows speed and the vertical axis the number of days at each speed. Note
that Columbus’s speed varied greatly, perhaps largely a reflection of the
varying wind and sailing conditions.

Bounty to Tahiti provides an
example in which astronomical fixes and dead reckoning played an important role
in navigation. After having sailed halfway around the world, some of Bligh’s
crew mutinied, putting the captain and his loyal crewmembers to sea, in a small boat near Tahiti.

While on the Bounty, Captain Bligh
had access to an accurate clock that kept Greenwich, England, time so that as
he sailed, he could compute his longitude based on the time difference between
solar noon and Greenwich time. Because Earth rotates once (360o) in
24 hours, every degree in longitude is equivalent to a time shift of solar noon
relative to Greenwich of 24 hr/360o or 4 minutes of time per degree
of longitude. Bligh had to bring a clock along on his voyage to keep in time
with Greenwich. Today, Greenwich time has been replaced by Universal time and
we can find the current Universal time over the Internet (http://aa.usno.navy.mil/faq/docs/UT.html).

After the mutiny, Bligh and the
loyal members of his crew, deprived of access to a clock, used estimates of his
small sailboat’s speed and direction to estimate degrees of longitude and
latitude referenced to a nearby islands and landmarks.

Use Captain Bligh’s diary from his voyage to reproduce a portion of his
travels. The text of his diary is available in an interactive Bounty Log form, pictured
below. Using Bligh's words, we track a portion of his voyage and learn about
his magnetic variation measurements.

Select
one of the following date links. The links will produce a map on which you may
plot Bligh’s voyage.

Access
Bligh’s diary for the month by using Select
Date on the form and pressing the GO button. The diary text for the month will appear in the Text Selection area. Search through the
diary text for Captain Bligh’s longitude, latitude and magnetic variation
(magnetic variation is the same as magnetic declination) values. Each should be
converted to decimal degrees using the Degree,
Minutes, Seconds, and Converter.

For
the locations where the magnetic variation is available, compare its value to
the predictions of the magnetic model in Voyager Model.

14. Fill in Table 2 with your data.

Table 2 - Tracking Captain
Bligh

Date

Longitude

Latitude

Magnetic Variation

Degrees (o) Minutes
(‘)

Decimal

Degrees (o) Minutes
(‘)

Decimal

Degrees (o) Minutes
(‘)

Decimal

15. During your selected month, trace Captain Bligh’s voyage on the map. Draw
arrows to show his direction of travel on the map below.

Imagine floating objects on the ocean surface, such as a bottle thrown in the
water. Test where it might travel based on the movement of currents.

Learn about ship cargo that has been lost at sea. Read examples of newsletters
by Curt Ebbesmeyer for the latest flotsam stories. Check the possible flotsam route with the ship
drift model.

Matrix for Grading Lesson 1

Proficiency Level

Description

4

Expert

Responses show an in-depth understanding of the models and
explorations used to explain the scientific concepts and processes used in
the lesson. Data collection and analyses are complete and accurate.
Predictions and follow through with accuracy of predictions are explained and
fully supported with relevant data and examples.

3

Proficient

Responses show a solid understanding of the models and
explorations used to explain scientific concepts and processes in the lesson.
Data collection and analyses are mostly complete and accurate. Predictions
and follow through with accuracy of predictions are explained and mostly
supported with relevant data and examples.

2

Emergent

Responses show a partial understanding of the models and
explorations used to explain the scientific concepts and processes in the
lesson. Data collection and analyses are partially complete and sometimes
accurate. Predictions and follow through with accuracy of predictions are
sometimes explained and supported with relevant data and examples.

1

Novice

Responses show a very limited understanding of the models
and analogies used to explain scientific concepts and processes in the lesson
Data collection and analyses are partially complete and sometimes accurate.
Predictions and follow through with accuracy of predictions are not well
explained and are not supported with relevant data and examples.